Necessary and sufficient conditions are given for the almost sure convergence of the quadratic form $\sum \sum f_{jk}M_jM_k$ where $(M_j)$ is a sequence of i.i.d. $p$-stable random variables. A connection is established between the convergence of the quadratic form and a radonifying property of the infinite matrix operator $(f_{kj})$.
Publié le : 1985-08-14
Classification:
Stable random variables,
quadratic forms,
$\theta_p$-radonifying operators,
60E07,
60B12
@article{1176992912,
author = {Cambanis, Stamatis and Rosinski, Jan and Woyczynski, Wojbor A.},
title = {Convergence of Quadratic Forms in $p$-Stable Random Variables and $\theta\_p$-Radonifying Operators},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 885-897},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992912}
}
Cambanis, Stamatis; Rosinski, Jan; Woyczynski, Wojbor A. Convergence of Quadratic Forms in $p$-Stable Random Variables and $\theta_p$-Radonifying Operators. Ann. Probab., Tome 13 (1985) no. 4, pp. 885-897. http://gdmltest.u-ga.fr/item/1176992912/